8434
2008, 112, 8434–8436 Published on Web 06/25/2008
NMR Studies of Molecular Conformations in r-Cyclodextrin ¨ stervall,†,‡ Kevin J. Naidoo,§,⊥ Johan Thaning,† Baltzar Stevensson,† Jennie O Go¨ran Widmalm,‡ and Arnold Maliniak*,† DiVision of Physical Chemistry Arrhenius Laboratory, Stockholm UniVersity, S-106 91 Stockholm, Sweden, Department of Organic Chemistry, Arrhenius Laboratory, Stockholm UniVersity, S-106 91 Stockholm, Sweden, Department of Chemistry, UniVersity of Cape Town, Rondebosch, 7701, South Africa, and Centre for High Performance Computing, CSIR Campus Rosebank, 7701 South Africa ReceiVed: March 28, 2008
A new approach for analysis of NMR parameters is proposed. The experimental data set includes scalar couplings, NOEs, and residual dipolar couplings. The method, which aims at construction of the conformational distribution function, is applied to R-cyclodextrin in isotropic solution and dissolved in a dilute liquid crystal. An attempt to analyze the experimental data using an average molecular conformation resulted in unacceptable errors. Our approach rests on the maximum entropy method (ME), which gives the flattest possible distribution, consistent with the experimental data. Very good agreement between experimental and calculated NMR parameters was observed. In fact, two conformational states were required in order to obtain a satisfactory agreement between calculated and experimental data. In addition, good agreement with Langevin dynamics computer simulations was obtained. Cyclodextrins (CDs) are cyclic R-(1f4)-linked carbohydrate oligomers constructed from glucose units.1 The smallest homologue is R-CD, Figure 1, followed by β- and γ-CDs, which comprise 6, 7, and 8 units of a glucopyranose monomer, respectively. Due to their unique structural features, these molecules are invaluable in a variety of industrial applications. Almost all applications involve the ability of the CDs to alter the physical, chemical, and biological properties of guest molecules through the formation of inclusion complexes.1 It is therefore of utmost importance to determine details of the molecular structure of cyclodextrins in general and conformational transitions in particular. The new method, described here, aims at construction of conformational distribution functions for complex molecules in isotropic solution and in a dilute liquid crystal. In the present letter, we investigate the conformational properties of R-CD using NMR spectroscopy and computer simulations. The ultimate goal in the description of the molecular structure is the determination of conformational probability distributions, P(φ,ψ), where the two torsion angles, φ and ψ, are related to the glycosidic linkage, Figure 1. Using experimental NMR parameters such as J couplings, NOEs, and residual dipolar couplings (RDCs), we determine the torsion angle distribution function for R-CD. However, defining the structure of carbohydrates still poses problems since usually only a limited number of NMR observables are possible to obtain. * To whom correspondence should be addressed. E-mail: arnold.maliniak@ physc.su.se. † Division of Physical Chemistry Arrhenius Laboratory, Stockholm University. ‡ Department of Organic Chemistry, Arrhenius Laboratory, Stockholm University. § University of Cape Town. ⊥ CSIR Campus Rosebank.
10.1021/jp802681z CCC: $40.75
Figure 1. Schematic of R-cyclodextrin.
It is so because severe spectral overlap, even at high magnetic fields, prevents sufficient resolution of many individual resonances. The second limitation is the fact that carbohydrates, rather than exhibiting a single well-defined structure, must be characterized by a distribution of conformations,2 which in turn requires an increased number of experimental data.3,4 In addition to the experimental investigations, we have carried out Langevin dynamics (LD) computer simulations of R-CD. Several computational investigations of the hydration effects and conformational properties of CDs have been previously reported.5–8 In oligosaccharides, the major degrees of freedom are related to bond rotations at the glycosidic torsion angles φ and ψ. These rotations are however significantly restricted in macrocyclic compounds such as the cyclodextrins. In initial tests, we assumed that the CD can be described as a uniaxial molecule exhibiting a single conformational structure. It turned out, however, that this analysis produced unacceptable errors in comparison with the experimental data for all three types of parameters. Therefore, we increased the sophistication level of the model 2008 American Chemical Society
Letters
J. Phys. Chem. B, Vol. 112, No. 29, 2008 8435
Figure 2. Contour map derived for R-CD, where φ ) H1′-C1′-O4-C4 and ψ ) C1′-O4-C4-H4. The shaded areas in (a) and (b) represent Prep(φ,ψ), which corresponds to the sterically allowed region. The distribution functions, PLC(φ,ψ), were determined using (a) the ME procedure (eq 2) with Prep(φ,ψ) ) 1, (b) as in (a) but with Prep(φ,ψ) ) exp{-Urep(φ,ψ)/kBT} (see text), and (c) the distribution function calculated from the LD trajectory, Ptraj(φ,ψ) (collision frequency12 γ ) 50 ps-1). The simulation was carried out for 5 ns at 300 K using CHARMM (parallel version, C27b4)13 employing a CHARMM22 type of force field, modified for carbohydrates and referred to as PARM22/SU01.14
and considered the maximum entropy (ME) method,9,10 which allows for continuous bond rotations. This approach is physically more sound than the average molecular conformation approximation. The ME analysis introduced here is carried out in two consecutive steps: First, we use the NMR parameters determined in the isotropic phase, that is, the scalar (3Jφ and 3J ) couplings and the NOEs (σ, related to r-6), for determiψ nation of Piso(φ,ψ)
{
-1 Piso(φ, ψ) ) Z iso Prep(φ, ψ)exp -
∑ λij3Jij(φ, ψ)ij
∑ λklrkl-6(φ, ψ)} (1) kl
where the adjustable parameters λij and λkl are determined by bringing calculated scalar couplings and NOEs into agreement with experimental observables, and Prep(φ,ψ) accounts for possible steric repulsions in the molecule. Second, the liquid crystal distribution function is constructed by using RDCs with conformation independent distance10 -1 PLC(β, γ, φ, ψ) ) Z LC Piso(φ, ψ) ·
{
exp -
∑ λmndmn(β, γ, φ, ψ)} (2) mn
where dmn(β,γ,φ,ψ) is the orientation- and conformationdependent dipolar coupling and β and γ are Euler angles specifying relative orientations of molecular and liquid crystal director frames. Ziso and ZLC are normalization factors. The conformational dependence of the dipolar couplings with a constant spin-spin distance originates from the fact that the orientational order is always conformation-dependent. Using PLC(β,γ,φ,ψ), we can calculate the averages of the RDCs
〈d〉 )
∫ d(β, γ, φ, ψ)PLC(β, γ, φ, ψ)sin β dβdγdφdψ (3)
The isotropic parameters, 3Jij(φ,ψ) and r-6 kl (φ,ψ), are averaged in an analogous way using Piso(φ,ψ). The strategy used in the analysis is to fit the experimental NMR parameters shown in Table S1 of the Supporting Information to eq 3. The distribution function PLC(β,γ,φ,ψ) is constructed using the λij, λkl, and λmn parameters. The fitting was performed by employing a computer code written in-house based on the MATLAB subroutine fminu.11 The λ parameters derived from the numerical fitting are collected in Table S2 of the Supporting Information. In Figure 2a, the distribution function PLC(φ,ψ) is displayed (note that the orientational variables β and γ have been integrated
out). Three peaks are observed in the distribution, with the global maximum located at {φ,ψ} ) {0°,0°}. The PLC(φ,ψ) distribution is essentially identical to the Piso(φ,ψ) probability (not shown). In principle, the analysis of experimental NMR parameters, that is, J couplings and NOEs, determined for the glycosidic angles φ and ψ will always result in a symmetric distribution function PLC(φ,ψ). In an attempt to eliminate possible sterical clashes, the available conformational space with atomic distances larger than 1.5 Å was determined. In practice, the steric interactions were described by short-range repulsion (including the Boltzmann factor), Prep(φ,ψ) ) exp{-Urep(φ,ψ)/kBT}, where Urep(φ,ψ) ) 12 ∑pq εpq(rmin pq /rpq) , and the parameters were taken from the CHARMM22 force field.13 The permitted region Prep(φ,ψ) is indicated in Figure 2a and b as the shaded areas. Clearly, in Figure 2a, the conformation corresponding to {φ,ψ} ) {70°,-80°} is located outside of the allowed region, and the symmetry-related state {φ,ψ} ) {-70°,80°} is located at the border of that region. We have therefore included Prep(φ,ψ) as a penalty term in eq 1. The distribution obtained by including this repulsion is shown in Figure 2b. Indeed, the conformation corresponding to {φ,ψ} ) {70°,-80°} is absent, and the {φ,ψ} ) {-70°,80°} state is slightly shifted. The global maxima in Figure 2a and b constitute 75% of each (total) population. The calculated values of the experimental parameters displayed in Figure 3 were obtained using eq 3 and PLC(φ,ψ) or Piso(φ,ψ). The agreement is good; in particular, the conformationdependent dH1′-H4 coupling not used in the analysis is accurately reproduced using PLC(φ,ψ). The conformational dependence of this coupling is shown in Figure 4; the calculated average is 2.66 compared to the experimental value of (2.60(50) Hz. Finally, in Figure 2c, we show the torsion angle distribution calculated from the trajectory generated in the LD computer simulation, Ptraj(φ,ψ). This distribution is indeed similar to that shown in Figure 2b derived from the experimental NMR parameters; in addition to the global maximum at {φ,ψ} ) {0°,0°}, a broad peak is observed. In contrast to the distribution derived from the experimental parameters, Ptraj(φ,ψ) does not exhibit a local minimum between the maxima. It can also be pointed out that while the analysis of the experimental data does not include the explicit ring structure of the CD molecule, the computer simulation contains this restriction. In conclusion, we have shown that it is possible to obtain the conformational distribution function, PLC(φ,ψ), for R-CD using NMR parameters, which included residual dipolar couplings (RDCs), cross-relaxation rates, and scalar J couplings.
8436 J. Phys. Chem. B, Vol. 112, No. 29, 2008
Letters ences of oligo- and polysaccharides. The fact that the conformational distribution for R-CD exhibits two conformational states may have important consequences for cyclodextrins forming inclusion complexes. Acknowledgment. Drs J.-C. P. Gabriel and H. Desvaux are gratefully thanked for a sample of V2O5 in D2O. We thank Patric Schyman for DFT-optimized coordinates of R-CD. This work was supported by grants from the Swedish Research Council and SIDA/SAREC. Supporting Information Available: Experimental procedure, experimental values (Table S1), and parameters derived from the ME analysis (Table S2). This material is available free of charge via the Internet at http://pubs.acs.org.
Figure 3. Comparison of observed and calculated NMR parameters for R-CD (RDCs: 1H-13C (squares), 1H-1H (crosses), J couplings (circles) in Hz; proton-proton distances rNOE (triangles) in Å). The liquid crystalline phase: V2O5 in D2O suspension.15 NMR experiments performed at 14.1 and 18.8 T: 2D 1JC,H-modulated 13C,1H CT-HSQC,16 2D 1H,1H COSY,17,18 1D DPFGSE 1H,1H T-ROESY.19 The experimental details are collected in the Supporting Information.
Figure 4. The conformational dependence of the residual dipolar coupling, dH1′-H4(φ,ψ). The maximum corresponds to the conformation with a short distance between H1′ and H4, and the negative values originate from the ordering tensor. The calculated average of this interaction is 2.66 Hz, which is well within the experimental uncertainty of (2.60(50) Hz.
The analysis rests on the maximum entropy (ME) approach applied in two steps. Our results are of special interest due to the well-known difficulty in describing conformational prefer-
References and Notes (1) Dodziuk H. Cyclodextrins and Their Complexes: Chemistry, Analytical Methods, Applications; Wiley: London, 2006. (2) Yi, X. B.; Venot, A.; Glushka, J.; Prestegard, J. H. J. Am. Chem. Soc. 2004, 126, 13636–13638. (3) Stevensson, B.; Landersjo¨, C.; Widmalm, G.; Maliniak, A. J. Am. Chem. Soc. 2002, 124, 5946–5947. ¨ stervall, J.; So¨derman, (4) Landersjo¨, C.; Stevensson, B.; Eklund, R.; O P.; Widmalm, G.; Maliniak, A. J. Biomol. NMR 2006, 35, 89–101. (5) Koehler, J. E. H.; Saenger, W.; van Gunsteren, W. F. J. Mol. Biol. 1988, 203, 241–250. (6) Lipkowitz, K. B. Chem. ReV. 1998, 98, 1829–1873. (7) Naidoo, K. J.; Chen, J. Y. J.; Jansson, J. L. M.; Widmalm, G.; Maliniak, A. J. Phys. Chem. B 2004, 108, 4236–4238. (8) French, A. D.; Johnson, G. P. Carbohydr. Res. 2007, 342, 1223– 1237. (9) Catalano, D.; Di Bari, L.; Veracini, C. A.; Shilstone, G. N.; Zannoni, C. J. Chem. Phys. 1991, 94, 3928–3935. (10) Berardi, R.; Spinozzi, F.; Zannoni, C. J. Chem. Phys. 1998, 109, 3742–3759. (11) MATLAB; The MathWorks Natick: MA, 1999. (12) Widmalm, G.; Pastor, R. W. J. Chem. Soc., Faraday Trans. 1992, 88, 1747–1754. (13) Brooks, B. R.; Bruccoleri, R. E.; Olafson, B. D.; States, D. J.; Swaminathan, S.; Karplus, M. J. Comput. Chem. 1983, 4, 187–217. (14) Eklund, R.; Widmalm, G. Carbohydr. Res. 2003, 338, 393–398. (15) Desvaux, H.; Gabriel, J. C. P.; Berthault, P.; Camerel, F. Angew. Chem., Int. Ed. 2001, 40, 373–376. (16) Tjandra, N.; Bax, A. J. Magn. Reson. 1997, 124, 512–515. (17) Delaglio, F.; Wu, Z. R.; Bax, A. J. Magn. Reson. 2001, 149, 276– 281. (18) Lycknert, K.; Maliniak, A.; Widmalm, G. J. Phys. Chem. A 2001, 105, 5119–5122. (19) Kjellberg, A.; Widmalm, G. Biopolymers 1999, 50, 391–399.
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